Mechanical regulation of endocytosis by protein condensate capillary forces

Max Ferrin

Clathrin-mediated endocytosis (CME)

(Lacy et al., 2018)

the cellular system I studied in my PhD is called clathrin mediated endocytosis (abbreviated to CME), which is the primary pathway for internalization of extracellular and membrane cargo in eukaryotic cells
what this looks like morphologically is diagrammed in this cartoon, which is a cross-section through a eukaryotic cell's plasma membrane
a small patch of plasma membrane and associated cargo is pulled into the cytoplasm and pinched off to result in an endocytic vesicle
concurrent with this is the sequential recruitment of endocytic proteins, which following an initial variable period, all appear with very very predictable timing to assist in the generation of the endocytic vesicle
while members of the lab study many aspects of CME from structure and biochemistry to physiology, my own research has focused on the mechanical forces at play

Mounting evidence of CME proteins forming liquid-like condensates

(Li et al., 2012; Bergeron-Sandoval et al., 2021; Day et al., 2021; Kozak and Kaksonen, 2022)

Condensates can deform membranes through capillary forces

(Kusumaatmaja et al., 2021)

an intrinsic property of liquid-like condensates is force experienced at interfaces
these are commonly referred to as capillary forces, and they are higher-order forces arising out of individual molecular interactions
molecules within the condensate have more energetically favorable interactions with each other than with the surrounding cytosol, so in bulk that results in a surface tension driving the condensate to minimize its contact area with the surrounding cytosol
condensate molecules can also have favorable interactions with a membrane, which in bulk causes a wetting potential driving it to maximize its contact area with the membrane
from examples in other systems, we know these capillary forces can be strong enough to deform membranes
there are several examples of a variety of protein condensate and membrane system that look like this: the wetting and surface tension drive the membrane to wrap around the condensate

by definition, when a solution phase-separates, new interfaces are created between the condensed phase and dilute phase, as well as with a surface if that's present
these interfaces experience interfacial forces, which are commonly referred to as capillary forces
in liquid-like condensates and membranes, the relevant capillary forces are surface tension of the condensed-dilute phase interface and wetting at the condensed phase-membrane interface
- these are higher-order emergent properties arising from building block interactions: condensed phase proteins have more energetically favorable interactions with themselves and with the membrane than with the solute in the dilute phase
in this particular example of storage vacuoles of arabidopsis embryos, we see that these forces lead to deformation of the vacuolar membrane

How does capillarity influence endocytic membrane bending?

Two complementary modeling approaches

Toy geometrical model	Continuum membrane mechanics model

everything is a spherical cap	discretized shapes governed by local forces
can be solved analytically	must be simulated numerically
relatively easy to write out and program	complicated math and simulation techniques required
unrealistic membrane shapes and kinks	realistic membrane curvature
purely equilibrium solution	can simulate temporal dynamics

Mechanical influence of condensate in toy model

so in order to gain that predictive understanding of these forces in isolation, I took a theoretical modeling approach to model the mechanical energy of a condensate during endocytosis
on the left is a 3d visualization of the model I built which consists of a membrane invagination in blue that can transition from flat to spherical, and a liquid protein condensate in green surrounding it
there's only 1 variable to keep track of in this talk which is h, the relative invagination distance from 0 (flat) to 1 (spherical)
based on the geometry at every point of h, I can calculate the change in free energy of individual components:
- positive free energy is unfavorable, negative is favorable
- surface tension of condensate-cytosol interface
- wetting energy of condensate-membrane interface
- membrane tension from pulling in membrane
- bending energy from spontaneous curvature of protein-coated invagination
- turgor pressure from volume of invagination
- all of these get added up into the sum for the whole system
in this particular set of parameters, endocytosis is energetically favorable

Condensate can provide net assistive force through wetting

Condensate surface tension results in energy barrier to initiation of membrane bending

The condensate can never be assistive to the flat-curved membrane transition

Droplet volume sets the energy barrier amplitude and position

Droplet volume sets the energy barrier amplitude and position

Summary: Condensate capillary forces inhibit membrane bending initiation, but assist completion

so in putting it all together, I have revealed a few forces that arise from condensate-membrane interactions
a condensate resists bending of a flat membrane into the condensate, but that force becomes weaker as the condensate volume increases
after bending is initiated, the system passes the energy barrier and the condensate can drive toward a net decrease in free energy
this leads to a potential physiological function of a condensate early in CME:
a condensate could slow things down during initiation while the machinery and cargo are accumulating, but drive toward complete invagination after a certain threshold
this is consistent with what we know about CME initiation being highly variable, followed by very reliable timing of internalization
this is the minimal story I have so far, but I have been putting in a lot of work to make it more complete

Aside: Different behavior in constant coat area vs. constant curvature alternative models

Aside: Free energy landscape of constant coat area vs. constant curvature alternative models

Validation of toy model results with continuum mechanics model

Toy geometrical model	Continuum membrane mechanics model

Supplement: coated membrane stabilizes at predicted curvature

Supplement: condensate stabilizes at predicted contact angle

Results in progress: complementary simulations to toy model

Model condensate stalls initiation of membrane bending at similar parameter regimes between models

Physiological significance of condensate mechanics

Under which parameter regimes is there a large vs. negligible effect from the condensate?
Which regime do experimental measurements place an endocytic condensate?
What parameters of the model might change over time in situ that could serve as regulatory features?

Results in progress: analysis of condensate's competition with coat bending energy

Hypothetical panel: comprehensive analysis of condensate impact on CME energy

Hypothetical panels: experimental estimation of condensate model parameters

(Brangwynne et al., 2009; Kozak and Kaksonen, 2022)

Hypothetical panel: regulatory potential of condensate mechanics

Thank you!

Summary: Condensate capillary forces inhibit membrane bending initiation, but assist completion

so in putting it all together, I have revealed a few forces that arise from condensate-membrane interactions
a condensate resists bending of a flat membrane into the condensate, but that force becomes weaker as the condensate volume increases
after bending is initiated, the system passes the energy barrier and the condensate can drive toward a net decrease in free energy
this leads to a potential physiological function of a condensate early in CME:
a condensate could slow things down during initiation while the machinery and cargo are accumulating, but drive toward complete invagination after a certain threshold
this is consistent with what we know about CME initiation being highly variable, followed by very reliable timing of internalization
this is the minimal story I have so far, but I have been putting in a lot of work to make it more complete

References

Bergeron-Sandoval, L.-P. et al. (2021) “Endocytic proteins with prion-like domains form viscoelastic condensates that enable membrane remodeling,” Proceedings of the national academy of sciences, 118(50). Available at: https://doi.org/10.1073/pnas.2113789118.

Brangwynne, C.P. et al. (2009) “Germline P Granules Are Liquid Droplets That Localize by Controlled Dissolution/Condensation,” Science, 324(5935), pp. 1729–1732. Available at: https://doi.org/10.1126/science.1172046.

Day, K.J. et al. (2021) “Liquid-like protein interactions catalyse assembly of endocytic vesicles,” Nature cell biology, 23(4), pp. 366–376. Available at: https://doi.org/10.1038/s41556-021-00646-5.

Kozak, M. and Kaksonen, M. (2022) “Condensation of Ede1 promotes the initiation of endocytosis,” Elife. Edited by M.I. Geli, 11, p. e72865. Available at: https://doi.org/10.7554/eLife.72865.

Kusumaatmaja, H. et al. (2021) “Wetting of phase-separated droplets on plant vacuole membranes leads to a competition between tonoplast budding and nanotube formation,” Proceedings of the national academy of sciences, 118(36), p. e2024109118. Available at: https://doi.org/10.1073/pnas.2024109118.

Lacy, M.M. et al. (2018) “Molecular mechanisms of force production in clathrin-mediated endocytosis,” Febs letters, 592(21), pp. 3586–3605. Available at: https://doi.org/10.1002/1873-3468.13192.

Li, P. et al. (2012) “Phase transitions in the assembly of multivalent signalling proteins,” Nature, 483(7389), pp. 336–340. Available at: https://doi.org/10.1038/nature10879.